The vertical axis shows the innovation effectiveness in the firms they surveyed, and the horizontal shows the number of innovation collaborations they have. It shows that adding innovation partners makes firms more innovative, up to about 11 partnerships. After that, adding more partners erodes performance.

The key question is why does it turn back down? This upside-down U shape is actually a very common research finding. You frequently see it in systems that require attention. Keld and Ammon think that in this case, it means that if you have too many partners, you can't pay enough attention to each, and your results start to get worse.

Edith Penrose found a similar effect in her great research back in the 1950s. She showed that there is a limit to managerial attention. This is what makes it hard to manage more than one business model within the same firm, why teams work best with no more than 8-12 people in them, and why there is a limit to any span of managerial control.

As you can see from the chart, the folks who fared the best — by a wide margin — were the in the modulated middle. They're called "ambiverts," a term that has been in the literature since the 1920s. They're not overly extroverted. They're not overly introverted. They're a little of both.

This is interesting for a couple of reasons. One is that we often search for black and white answers - but business rarely offers them. Is collaboration good? Yes, but only up to a point. Is extroversion good if you're a salesperson? Yes, but only up to a point.

Figuring out where that point lies is part of the art of managing. And being comfortable with the ambiguity in this is an even bigger part of that art.